Please help explain the solution, thank you! An amusement park lets guests drive

Question

Please help explain the solution, thank you!

An amusement park lets guests drive their own cars over 400 acres of land. At the entrance, a sign warns tourists that there is a 65% chance that a car will take some damage by an animal during the visit. Suppose 20 cars are selected at random and 18 cars have some damage. Does it appear that the population proportion of cars with some damage exceeds the park’s claim? The hypotheses to be tested are H0: p = 0.65 versus Ha: p > 0.65, where the parameter p represents the population proportion of all cars that have some damage from an animal after the safari drive-thru.

What is the observed value of the test statistic for testing the hypotheses for this study?

-If the null hypothesis is true, what is the distribution of the test statistic (which distribution should be used to find the p-value)?

-What is the correct corresponding p-value for this test?

-Our decision at the 5% level of significance is to reject the null hypothesis. Based on our decision, the appropriate conclusion in context is:

a)There is not sufficient evidence to conclude that the sample proportion of cars with some damage exceeds the park’s claim.

b) There is not sufficient evidence to conclude that the population proportion of cars with some damage exceeds the park’s claim.

c) There is sufficient evidence to conclude that the sample proportion of cars with some damage exceeds the park’s claim.

d) There is sufficient evidence to conclude that the population proportion of cars with some damage exceeds the park’s claim.

If the study will be repeated in the future with the same sample size selected from the sample population, but now a 10% significance level will be used, then the probability of correctly rejecting the null hypothesis would (decrease, increase, or stay the same)?

Explanation / Answer

Ans:

sample proportion=18/20=0.9

sampling distribution of sample proportions folllow normal distrbution.

Test statistic:

z=(0.9-0.65)/sqrt(0.65*(1-0.65)/20)=2.34

p-value=P(z>2.34)=0.0096

As,p-value<0.05,we reject null hypothesis.

Option d is correct.

There is sufficient evidence to conclude that the population proportion of cars with some damage exceeds the park’s claim.

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